Chaotic and periodic natural convection for moderate and high Prandtl numbers in a porous layer subject to vibrations

Abstract

The analysis of natural convection for moderate and high Prandtl numbers in a fluid-saturated porous layer heated from below and subject to vibrations is presented with a twofold objective. First, it aims at investigating the significance of including a time derivative term in Darcy’s equation when wave phenomena are being considered. Second, it is dedicated to reporting results related to the route to chaos formoderate and high Prandtl number convection. The results present conclusive evidence indicating that the time derivative term in Darcy’s equation cannot be neglected when wave phenomena are being considered even when the coefficient to this term is extremely small. The results also show occasional chaotic “bursts” at specific values (or small range of values) of the scaled Rayleigh number, R, exceeding some threshold. This behavior is quite distinct from the case without forced vibrations, when the chaotic solution occupies a wide range of R values, interrupted only by periodic “bursts.” Periodic and chaotic solution alternate as the value of the scaled Rayleigh number varies.